Evan Rodrigues was born on July 28, 1993, in Toronto, Ontario. He played junior hockey for the Georgetown Raiders of the OJHL before attending Boston University. In two seasons at BU, Rodrigues was a two-time Hockey East Second Team All-Star and during his senior year, he was the NCAA's second leading scorer with 61 points.

On April 22, 2015, Rodrigues agreed to an entry-level contract with the Buffalo Sabres. He would spend the majority of the 2015-16 season with the Rochester Americans of the American Hockey League before receiving his first NHL call-up. He made his NHL debut on April 8, 2016 and recorded his first goal and first assist the following night.

Rodrigues would split time between Rochester and Buffalo during the 2016-17 season. In 30 games at the NHL level he scored four goals and added a pair of assists.